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10 Nov 2019
Prove the equivalence between the statements.
Let A be an nxn matrix. There are many statements equivalent to the statement "A has nonzero determinant" is one of them. Here are nine others: The system .Ax = 0 has only the trivial solution. The column vectors of .4 are linearly independent. The row vectors of A are linearly independent. The column vectors of A span Rn. The row vectors of A span Rn. The column vectors of .4 form a basis for The row vectors of .A form a basis for Rn. A has rank n. A has nullity 0. In the following nine short exercises, you will prove that these nine statements by showing that
Prove the equivalence between the statements.
Let A be an nxn matrix. There are many statements equivalent to the statement "A has nonzero determinant" is one of them. Here are nine others: The system .Ax = 0 has only the trivial solution. The column vectors of .4 are linearly independent. The row vectors of A are linearly independent. The column vectors of A span Rn. The row vectors of A span Rn. The column vectors of .4 form a basis for The row vectors of .A form a basis for Rn. A has rank n. A has nullity 0. In the following nine short exercises, you will prove that these nine statements by showing that
Lelia LubowitzLv2
25 Sep 2019